Set Puzzle

Hello friends:

Can anyone solve my below mentioned maths problem...

Consider a set with 256 numbers (May be integer ,real , etc).

First step:

1) From the set of 256 numbers, Pick any 3 numbers
2) Apply some calculation on the picked numbers to generate 2 numbers (Converting 3 numbers to 2 numbers).
3) The 2 Numbers should be part of the original set

Second step:

To reverse the process, i.e, Converting this 2 Numbers to the original 3 Numbers back.

1) Take the same 2 numbers
2) Apply some calculation on the these numbers and get back the original numbers (3 numbers) in the same sequence.

EXAMPLE:

(1,2,3,4....256) - Original Set

(2,55,255) - Random pick from the above set

(75,155) - Calculating with formula from the above 3 numbers and derive 2 numbers which will pe part of the original set.

(2,55,255) - Doing reverse calculation of the above 2 numbers and derive the same 3 numbers.

I would be glad if someone can get an answer and send it to me (kanthss@gmail.com).

1) From the set of 256 numbers, Pick any 3 numbers
2) Apply some calculation on the picked numbers to generate 2 numbers (Converting 3 numbers to 2 numbers).
3) The 2 Numbers should be part of the original set

Second step:

To reverse the process, i.e, Converting this 2 Numbers to the original 3 Numbers back.

1) Take the same 2 numbers
2) Apply some calculation on the these numbers and get back the original numbers (3 numbers) in the same sequence.

EXAMPLE:

(1,2,3,4....256) - Original Set

(2,55,255) - Random pick from the above set

(75,155) - Calculating with formula from the above 3 numbers and derive 2 numbers which will pe part of the original set.

(2,55,255) - Doing reverse calculation of the above 2 numbers and derive the same 3 numbers.

I would be glad if someone can get an answer and send it to me (kanthss@gmail.com).

Thanks and regards,
Srikanth

What is the question?

The observation I would make is that there can be no such formula, since
it maps a set with 256^3 points into a set with 256^2 points, so each
point in the image must correspond to more than one point in the original
set and so it cannot be invertible.